Since many of you will be taking Calc 2 (MAT1575) this upcoming semester, here are some resources to help you prepare for that course:
Recall that the central idea of Calc 1 – MAT1475 was the derivative of a function, and we found the derivatives of various functions and developed various differentiation rules (the power rule, the sum rule, the product rule, the quotient rule, the Chain Rule). You should start by reviewing some basic derivatives!
The central idea of of Calc 2 – MAT1575 is the (indefinite) integral, which is the term for “antiderivatives”: for a given function f(x), find a function whose derivative is f(x).
I recommend getting familiar with the idea of antiderivaties and the “integral notation” for antiderivatives, and working through some basic examples. You can download the following math department workbook and study Sections 1 (“Review of Derivatives”) and Section 2 (“Antiderivatives”):
You can also look over Sec 4.10 of the OpenStax textbook, which introduces antiderivatives and the terminology and notation of indefinite integrals. Here is a table from that section with a list of of derivatives in the left column, which you should recognize from MAT1475, and the corresponding antiderivatives, in the integral notation:
Here is a Khan Academy video which introduces the concept and notation for antiderivatives, via some basic examples:
Further videos and exercises on basic antiderivatives can be found in this Khan Academy calculus course unit (and also the following unit).
Just as the main application/motivation of derivatives in MAT1475 was the geometric concept of finding tangent lines (and the physical concept of instantanteous velocity), antiderivatives have geometric and physical applications and motivations as well: finding the area under a curve, or finding distance travelled from the velocity function. These are called definite integrals, and are covered in Section 3 of the CityTech workbook.
You can also watch this 3blue1brown video which illustrates these concepts:
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